On some classical radicals for special Lie algebras (Q2862862)
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scientific article; zbMATH DE number 6228952
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some classical radicals for special Lie algebras |
scientific article; zbMATH DE number 6228952 |
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19 November 2013
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representations of Lie algebras
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On some classical radicals for special Lie algebras (English)
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A Lie algebra \(L\) is special in the sense of V. N. Latyshev if there exist an associative PI-algebra \(A\) and an embedding of \(L\) into the Lie algebra \(A^{(-)}\). For a special Lie algebra \(L\) denote by \(N(L)\) the intersection of maximal locally nilpotent ideals for all PI-representations of \(L\). It is shown that Braun-McCoy radical of \(L\) contains prime radical \(P(L)\) and \(P(L)\) contains \(N(L)\). If the base field has characteristic zero, then Jacobson radical of \(L\) contains the intersection of annihilators of all PI-representations of \(L\).
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